Tip-enhanced nano-spectroscopy and -imaging, such as tip-enhanced photoluminescence (TEPL), tip-enhanced Raman spectroscopy (TERS), and others, have become indispensable from materials science to single molecule studies. However, the techniques suffer from inconsistent performance due to lack of nanoscale control of tip apex structure, which often leads to irreproducible spectral, spatial, and polarization resolved imaging. Instead of refining tip-fabrication to resolve this problem, we pursue the inverse approach of optimizing the nano-optical vector-field at the tip apex via adaptive optics. Specifically, we demonstrate dynamic wavefront shaping of the excitation field to effectively couple light to the tip and adaptively control for enhanced sensitivity and polarization-controlled TEPL and TERS, with performance exceeding what can be achieved by conventional tip-fabrication and optimal excitation polarization. Employing a sequence feedback algorithm, we achieve 4.4$times$10$^4$-fold TEPL enhancement of a WSe$_2$ monolayer which is >2$times$ larger than the normal TEPL intensity without wavefront shaping, as well as the largest plasmon-enhanced PL intensity of a transition metal dichalcogenide (TMD) monolayer reported to date. In addition, with dynamical near-field polarization control in TERS, we demonstrate the investigation of conformational heterogeneity of brilliant cresyl blue (BCB) molecules as well as the controllable observation of IR-active modes due to a large gradient field effect. Adaptive tip-enhanced spectroscopy and imaging thus provides for a new systematic approach towards computational nanoscopy making optical nano-imaging more robust, versatile, and widely deployable.
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